Ring laser having amplitude and phase controlled crossed-beam anti-locking feedback

ABSTRACT

A ring laser provided with at least one mirror external to the ring cavity for reflecting energy from one of the two counterrotating laser beams back into the ring to couple to the other beam. The mirror is arranged to have varying reflectivity along one of its dimensions and is positioned along said dimension (to vary the amplitude of feedback) and in a direction perpendicular thereto (to vary the phase of feedback). Each of the counterrotating laser beams is extracted from the cavity and the amplitude modulation thereon (due to cross-beam coupling) is detected. If two external mirrors are used, each is positioned to eliminate the amplitude modulation on a respective extracted beam. If only one external mirror is used, it is positioned to make the amplitude modulation on one extracted beam equal in amplitude and opposite in phase to the amplitude modulation on the other extracted beam.

United States Patent Macek et a1.

[54] RING LASER HAVING AMPLITUDE AND PHASE CONTROLLED CROSSED- BEAMANTI-LOCKING FEEDBACK [72] Inventors: Warren M. Macek, HuntingtonStation; Chao Chen Wang, Mineola, both of NY.

[52] US. Cl. ..356/106 LR, 331/94.5, 332/751 [51] Int. Cl. ..GOlb 9/02[58] Field of Search...88/l4 I; 331/945; 356/106 LR [56] ReferencesCited UNITED STATES PATENTS 4/1967 l-lufangel et a1....33l/94,5 UX6/1967 Killpatrick ..88/14I 51 Oct. 10,1972

Primary Examiner-Benjamin A. Borchelt Assistant bcaminer--N. MoskowitzAttorney-S. C. Yeaton [57] ABSTRACT A ring laser provided with at leastone mirror external to the ring cavity for reflecting energy from one ofthe two counterrotating laser beams back into the ring to couple to theother beam. The mirror is arranged to have varying reflectivity alongone'of' its dimensions and is positioned along said dimension (to varythe amplitude of feedback) and in a direction perpendicular thereto (tovary the phase of feedback). Each of the counter-rotating laser beams isextracted from the cavity and the amplitude modulation thereon (due tocross-beam coupling) is detected. If two external mirrors are used, eachis positioned to eliminate the amplitude modulation on a respectiveextracted beam. 11 only one external mirror is used, it is positioned tomake the amplitude modulation on one extracted beam equal in amplitudeand opposite in phase to the amplitude modulation on the other extractedbeam.

6 Claims, 6 Drawing Figures VOLT. SOURCE PATENTEnnm m 1912 3. 697. 1 81SHEEI1UF4 KBA AND KAB HERMITIAN COUPLING Aa KBA a SKEW HERMITIAN 6COUPLING O (c) (d) Fl 6. 1. FROM BEAM AMPLITUDE DETECTOR 2 SINTECZRZATOR j 85 DE L A Y PHASE SUMM NG C RCU [T DETECTOR C|RCu|T I TO86 MOTOR AMPLITUDE 29x DETECTOR l $53M 81 A INVENTORS WARREN M. MACEKF|G.5. Q I

ATTORNEY M'IENTED I0 I97! 3 697. 181

SHEEI 3 [IF 4 l f5? 58 Cl 59 20- b O I I L .55. c o 1 i 1 68 d O I I I II I g f O PATH OF RESPECTIVE /EXTERNAL FEEDBACK BEAM 4% PATH OFRESPECTIVE EXTERNAL FEEDBACK INVENTORS AZTOR/VEY PATENTEnum 10.1972 3.697. 1 8 1 saw u or 4 RING ROTATIONAL RATE -u AONHOOEHA ELLON .LVHE!INVENTORS WARREN M. MACEK CHAO CHE/V WANG BY ATTORNEY RING LASER HAVINGAMPLITUDE AND PHASE CONTROLLED CROSSED-BEAM ANTI-LOCKING FEEDBACK Theinvention herein described was made in the course of or under a contractor subcontract thereunder, with the Department of the Air Force.

BACKGROUND OF THE INVENTION As is well understood, ring lasers areemployed to sense rotation relative to an inertial frame of reference bydetecting the beat note or frequency difference between the twocounterrotating beams (two single beams which travel in oppositedirections around the ring). The frequency difference is proportional tothe rate of rotation; as the rate of rotation decreases, the beat notefrequency decreases toward zero. However, when the frequencies of thetwo counterrotating beams approach each other closely, there is anincreasing tendency toward mode locking to a common frequency. A certaincritical value of coupling exists between the two counterrotating beamsabove which the frequencies of the two beams will pull toward the samefrequency to produce a zero beat note. Such mode locking destroys theability of the ring laser to sense very low rotation rates and distortsthe relationship between beat note frequency and ring rotation rate asthe mode locking point nears.

Several factors contribute to the coupling between the counterrotatingbeams and the resulting mode locking within the ring laser. For example,passive light scattering from optical surfaces in both the forward andbackward directions and retro-reflection of transmitted light as well asnon-linear effects within the active laser medium have been demonstratedto be effective in producing frequency locking. Unavoidablebackscattering occurs from laser windows, corner reflectors, andcombining optics and detectors. High quality polished surfaces andnearly perfect dielectric coatings on mirrors can not prevent a smallamount of energy from one laser beam from being coupled or scattered inthe direction of the oppositely travelling beam. Finite bore sizing ofgas discharge tubes as well as apertures added to the ring to reducetransverse oscillating modes also contribute significantly to unwantedcrosscoupling between the laser beams which produce a mode pullinginstability and eventually a frequency locking effect.

Prior art attempts at solving the problem of mode locking have beendirected at either avoiding or minimizing the problem withouteliminating it. Mode locking can be avoided simply by introducing apredetermined frequency offset or bias between the two counterrotatingbeams in the ring laser. Such bias prevents the frequencies of the twobeams from approaching each other closely enough to cause mode lockingfor a specified range of rotation rates which the laser is known toencounter in a given application. Alternatively, the problem of modelocking can be significantly reduced by simultaneously frequencymodulating each of the counterrotating beams in a prescribed manner asset forth in copending patent application Ser. No. 597,761, filed onNov. 29, 1966, now U.S.1Pat. No. 3,462,708 in the name of Robert E.McClure and assigned to the present assignee.

SUMMARY OF THE INVENTION It has been found theoretically that scatteringforces within a ring laser which cause the mode locking of thecounterrotating beams always can be resolved into I-Iermitian and skewHermitian components. In general, for a given magnitude of scattering,skew Hermitian coupling is substantially more effective in producingmode locking than is I-Iermitian coupling. Apparatus is provided, inaccordance with a first aspect of the present invention, for theelimination of both the Hermitian and the skew Hermitian components witha consequent elimination of mode pulling. The Hermitian and skewHermitian components are eliminated by amplitude and phase controlledfeedback from each of the counterrotating beams to the other so that theamplitude modulation on each of the counterrotating beams (due tocross-coupling between the beams) is reduced to zero. In a second aspectof the invention, solely the skew Hermitian component is eliminated withthe aid of simpler apparatus to yield a very significant reduction inmode locking. The skew Hermitian component is eliminated by amplitudeand phase controlled feedback from one of the counterrotating beams tothe other so that the amplitude modulation on one of the counterrotatingbeams is made equal in amplitude and opposite in phase to the amplitudemodulation on the other beam.

BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 is a series of phasor diagramsrepresenting the Hermitian and skew Hermitian components of the couplingforce acting between the couterrotating beams of a ring laser;

FIG. 2 is a simplified diagram of a first species of the inventionwherein both the Hermitian and skew Hermitian components of the couplingforce are eliminated;

FIG. 3 is a series of waveforms helpful in understanding the embodimentof FIG. 2;

FIG. 4 is an enlarged view of some of the components shown in FIG. 2;

FIG. 5 is a simplified diagram of a second species of the inventionwherein solely the skew Hermitian component of the coupling force iseliminated; and

FIG. 6 is a plot depicting the mode locking characteristic of a typicalring laser with and without the benefit of the apparatus represented inFIG. 5.

DESCRIPTION OF THE PREFERRED EMBODIMENTS It can be shown that theresultant scattering force acting within a ring laser can be resolvedinto I-Iermitian and skew Hermitian components. By definition, thecoupling force acting on one of the laser beams (beam B) due to theother laser beam (beam A) can be represented by iK A and the couplingforce acting on beam A due to beam B can be represented by -iK B. Thefactor K in turn, can be expressed as lK I i KAa and the factor K can beexpressed as |K le-i BA. The coupling is Hermitian when K Typicallyfthecoupling resultTiffbrhFIdfT in a well designed ring laser is stronglyHermitian although some skew Hermitian coupling generally also ispresent. Skew Hermitian coupling is primarily responsible fpr modelockingbetween the counterrotating beams despite its ordinarily weakermagnitude relative to Hermitian coupling. Scattering from mirrors andwindows, for example, normally gives rise to Hermitian coupling whereaslosses in cavity mirrors cause skew I-Iermitian coupling. Hermitiancoupling generally can supply only reactive energy but not real energyto the coupled beams. Skew l-lermitian coupling, on the other hand,either consumes energy (if lossy) or produces energy (if an activemedium) but will not store energy. Thus, skew I-lermitian coupling addsor consumes real energy with respect to the coupled beams.

The distinctive characteristics of the Hermitian and the skew Hermitiancoupling force are depicted in the phasor diagrams of FIG. 1. Phasors Aand B of FIG. I represent respective counterrotating beams of the ringlaser. If the ring laser is rotating about an axis normal to I the planeof the ring, the frequency of the one beam increases while the frequencyof the other beam decreases from the common nominal frequency valuewhich obtains in the absence of ring rotation. The angular rotation rateof each phasor about origin represents the frequency of the respectivebeam whereas the amplitude of each phasor represents the amplitude ofthe respective beam.

In the presence of l-lermitian coupling between the laser beams, someenergy from each beam couples into the other as represented by thevectors K and K of FIGS. 1a and b. K represents the energy from beam Bwhich is coupled into beam A and K representing the energy from beam Awhich is coupled into beam B. The coupled component maintains a fixedphase relationship relative to the beam from which it derives itsenergy. For example, the coupled component K always maintains a fixedphase relationship relative to beam B because said component derives itsenergy from beam B. Similarly, the coupled component K maintains a fixedphase relationship relative to beam A. FIGla represents the illustrativecase wherein phasors A and B are of the same amplitude and momentarilyof the same phase while coupling forces K and K also are of the sameamplitude and momentarily of the same phase. Considering that the ringlaser is rotating so that phasors A and B rotate in the same directionbut at different angular rates about origin 0, the phasors will assumethe positions shown in FIG. lbat a subsequent time. It should be notedthat coupling force K maintains the same phase (angular) relationshipwith respect to phasor A as obtained in FIG. la. Similarly, couplingforce K maintains the same phase relationship relative to phasor B asobtained in FIG. 1a. Coupling force K may be resolved into components Iand 2 in the direction of and perpendicular to the direction of phasorB, respectively. Coupling force K may be resolved into components 3 and4 in the direction of and perpendicular to the direction of phasor A,respectively. As is characteristic of Hermitian coupling, the componentsI and 3 of the coupling forces K and K simultaneously act in oppositedirections upon the amplitudes of phasors I3 and A.

That is, the amplitude of phasor B is reduced by component 1 while theamplitude of phasor A is increased by component 3, i.e., the amplitudemodulations on the phasors A and B are out of phase. It should also benoted that the components 2 and 4 simultaneously change the angularrotation rates of phasors B and A in the same sense, i.e., either bothphasors A and B are accelerated or decelerated in angular rate bycomponents 4 and 2 whereby the frequency difference between phasors Aand B is unaffected by components 4 and 2.

FIGS. 10 and 1d represent the skew Hermitian coupling force actingbetween beams A and B. FIG. 10 represents the illustrative case whereinphasors A and B have the same amplitude and momentarily the same phasewhereas coupling forces K and K have the same amplitude and momentarilythe opposite phase. In the presence of the same angular ring rotation asin the case of FIG. lb, phasors A and B assume the positions shown inFIG. 1d at a moment subsequent to the time represented in FIG. 10. Itshould again be noted that the phase of coupling force K relative to thephasor B and the phase of coupling force K relative to phasor A are thesame in FIGS; 1(c) and FIG. 1d. Resolving the coupling forces K and Kinto their respective components 5, 6 and 7, 8, it can be seen thatcomponents 5 and 7 simultaneously act to decrease the amplitude ofphasors A and B whereas components 6 and 8 oppositely affect the angularrotation rates of phasors A and B. The angular rotation rates of phasorsA and B and, hence, the frequency difference therebetween continuouslychanges with time as phasors A and B rotate about origin 0, at differentrates due to rotation of the ring laser. Thus, frequency locking betweenthe two counterrotating ring laser beams is much more probable in thepresence of skew Hermitian coupling as compared to an equal magnitude ofI-Iermitian coupling.

In accordance with the first species of the invention, mode lockingbetween the counterrotating beams of a ring laser is eliminated bycompletely cancelling both the Hermitian and the skew Hermitiancomponents of the coupling force acting between the beams. This isaccomplished with the aid of the apparatus represented in FIG. 2 byreflecting back into the ring laser energy of proper phase and amplitudeto cancel each coupling component K and K discussed in connection withFIG. I. The required energy conveniently is obtained by the use of apair of mirrors 9 and 1e located outside of the closed loop optical pathof ring laser Ill. Each of the mirrors 9 and 10 reflect a respective oneof the counter-rotating beams which exits through the correspondingpartially transmitting corner reflector 12 or 13. Each of the mirrors 9and 10 are positioned by apparatus to be described along the directionof the impinging beam (so as to vary the phase of the reflected light)and along a second direction at right angles thereto (so as to vary theamplitude of the reflected light). The faces of the mirrors arepartially covered by an anti-reflection coating so that the effectivereflecting area encountered by the impinging beam (hence the amplitudeof the reflected light) is varied by movement of the mirror along theaforesaid second direction.

Ring laser 11 is of conventional design and comprises an active lasingmedium 14 and corner reflectors 12,

13, 15 and 16. Reflector 15, like reflectors l2 and 13, is partiallytransmitting to allow the counterrotating beams to emerge from the ringand be optically combined for the production of beat notes representingthe frequency difference between the two and, hence, the rotation rateof laser 11. The beat notes are derived with the aid of conventionalcombining optics comprising reflectors 17 and 18, beamsplitter 19 andphotocells 20 and 21. An electrical (beat) signal having a frequencyequal to the desired beat note is provided by each of photocells 20 and21.

In order to position mirrors 9 and 10 automatically, provision is madefor placing the beat note form photocell 20 in phase quadrature withrespect to the beat note from photocell 21. This is achieved through theuse of quarter waveplate 22 and polarizers 23 and 24. Ring laser 11produces a pair of linearly polarized counterrotating beams in aconventional manner. One of the beams (beam A) propagates in acounterclockwise direction whereas the other beam (beam B) propagates ina clockwise direction within the closed loop laser cavity. Beam A exitsthrough partially transmitting mirror 15 and is redirected by mirror 17and beamsplitter 19 to photocells 20 and 21. Polarizers 23 and 24 permitcomponents of beam A to impinge on photocells 20 and 21 in the same timephase. Beam B passes through partially transmitting mirror 15 and isconverted into a circularly polarized beam by quarter waveplate 22. Thecircularly polarized beam is redirected by mirror 18 and beamsplitter 19to polarizers 23 and 24. The circularly polarized beam B comprises twolinearly polarized components in time and space quadrature. Polarizer 23passes the first component to photocell 20. The second component ofcircularly polarized beam B is attenuated by polarizer 23. Said secondcomponent is passed by polarizer 24 which blocks the first component.Inasmuch as the components of beam B are in time phase quadrature withrespect to each other at photocells 20 and 21 and the components of beamA are in time phase with respect to each other at photocells 20 and 21,the beat note signal output from photocell 20 is in time phasequadrature with respect to the beat note signal output from photocell21.

Each of beams A and B is amplitude modulated in the presence of internalfeedback from the other beam which causes mode locking. The amplitudemodulation on beam A (due to cross-coupling from beam B) is detected byphotocell 25 whereas the amplitude modulation of beam B (due tocross-coupling from beam A) is detected by photocell 26. It will beobserved that solely beam A passes through mirror 12 to photocell 25 andsolely beam B passes through mirror 13 to photocell 26. The outputsignal from photocell 20 on line 27' and the output signal fromphotocell 21 on line 28 are used as reference signals against which thephases of the amplitude modulations on beam A (line 29) and on beam B(line 30) can be compared. The phase comparisons are made with the aidof phase detectors 31, 32, 33 and 34.

it is necessary to align the phases of the reference signals relative tothe phase of the amplitude modulation on beam A prior to positioningmirror 9. Similarly, it. is necessary to align the phases of thereference signals relative to the phase of the amplitude modulation onbeam B prior to positioning mirror 10. The steps are taken in sequenceunder the control of earns 90, 91, 92 and 93 and shutters 3S and 36 onshaft 94 driven by motor 50. Cams 90, 91, 92 and 93 actuate switches 95,96, 97 and 98, respectively, to produce gating signals in propersequence on lines 99, 100, 101, and 102, respectively. Switches 95 and96 receive excitation from source 103 whereas switches 97 and 98 receiveexcitation from source 104. In the first of the alignment steps, shaft94 is angularly displaced so that shutter 35 blocks its respectivefeedback beam and cam 90 closes switch 95. At the same time, switches96, 97 and 98 are open and shutter 36 does not block its respectivefeedback beam. Under the cited conditions, phase detector 31 provides anoutput signal to gate 37 representing the phase difference between thebeat note on line 27 and the amplitude modulation signal on line 29.Normally nonconducting gate 37 is rendered conductive by the signal online 99 and applies the phase error signal from detector 31 topiezoelectric crystal 40 via integrator 39. Crystal 40 serves toposition mirror 18 in accordance with the integral of the phase errorsignal from phase detector 31 until the output of phase detector 31 isreduced to a null. In the null condition, the beat note signal on line27 is in phase quadrature with respect to the amplitude modulationsignal on line 29. Consequently, the beat note signal on line 28 isplaced into an in phase relationship at phase detector 32 with respectto the amplitude modulation signal on line 29. This terminates thealignment mode of the apparatus represented in FIG. 2 prerequisite tothe positioning of mirror 9.

In the positioning mode, shutter 35 is rotated to permit theestablishment of the external feedback beam and mirror 9 issimultaneously positioned along two orthogonal directions to vary theamplitude and the phase of the external feedback beam so as to maintainthe previously obtained null output from phase detector 31 and drive theoutput from phase detector 32 to a null. At the same time that shutter35 is rotated to pass the feedback beam, camdisengages switch and cam 91actuates switch 96 to produce a gating signal on line 100. Said gatingsignal renders normally non-conducting gate 41 conductive to establish aconnection between phase detector 31 and integrator 42 which positionsmirror 9 along the axis of the external feedback beam via piezoelectriccrystal 106. Simultaneously, the gating signal on line 100 rendersnormally non-conducting gate 43 conductive to establish a connectionbetween the output of phase detector 32 and motor 44 which drives mirror9 in a direction transverse to the direction of the external feedbackbeam.

It will be recognized, of course, that the phase and the amplitude ofthe external feedback beam are entirely arbitrary at the moment that thebeam is established by the rotation of shutter 35 out of the path of theexternal feedback beam. In order to completely cancel the internalfeedback from beam B to beam A and thereby eliminate its contribution tomode locking between the counterrotating beams within the ring laser, itis necessary that the external feedback be made equal in magnitude andout of phase with respect to the internal feedback from beam B to beamA. If the external feedback was not in 180 phase relationship with theinternal feedback, then the null which was achieved at the output ofphase detector 31 during the alignment mode will be disturbed. A, signalof appropriate polarity at the output of phase detector 31 signifies thedirection in which the external feedback signal departs from the desired180 phase relationship with respect to the internal feedback signal. Theresulting phase error signal is applied via conducting gate 41 andintegrator 42 to piezoelectric crystal 106 which positions mirror 9 tovary the phase of the external feedback beam so as to restore the nullat the output of phase detector 31. At the same time, the amplitude ofthe external feedback signal is varied by the output signal from phasedetector 32 which drives motor 44 via conducting gate 43 in a directionto minimize the amplitude of the signal on line 29 representing the netfeedback from beam B to beam A resulting from both the internal and theexternal feedback.

The above described operation can be better understood by referring tothe waveforms of FIG. 3. The gating signal 58, appearing on line 99 ofFIG. 2, comprises a pedestal portion 57 having a duration coincid ingwith the alignment mode and a base portion 105 coinciding with thepositioning mode related to the adjustment of mirror 9. At the end ofthe alignment mode, there is no output from phase detector 31 (portion59 of wave form 60, FIG. 3b) but there is a maximum output from phasedetector 32 (portion 61 of waveform 62, FIG. 3e). If the arbitraryposition of mirror 9.is other than the correct one for completecancellation of the amplitude modulation on beam A as represented by theamplitude of the signal on line 29, one of the waveforms 60 and 64 ofFIG. 3b and FIG. 3c will appear at the output of phase detector 31 andone of the waveforms 62 and 66 of FIG. 3e and FIG. 3f will be producedat the output of phase detector 32. If the arbitrary position of mirror9 happens to be the correct one for complete cancellation of the signalon line 29, waveform 65 of FIG. 3d is produced at the output of phasedetector 311 and waveform 67 of FIG. 3g is produced at the output ofphase detector 32. It should be noted that portions 68 and 69 ofwaveforms 65 and 67 are at a null (zero amplitude) when mirror 9 hasbeen correctly positioned to completely cancel the signal on line 29.

Fully equivalent apparatus is provided for the positioning of mirror soas to provide external feedback of proper amplitude and phase tocompletely eliminate the amplitude modulation on beam B due to internalfeedback from beam A whereby the amplitude of the signal on line 30 isreduced to a null. The apparatus for this purpose comprises voltagesource 104, switches 97 and 98, gates 72, 73 and 74, shutter 36,integrators 39 and 75, phase detectors 33 and 34, piezoelectric crystal76 and motor '77. First, the signal on line 27 at the output ofphotocell is placed in phase quadrature with the signal on line 30 atthe output of photocell 26 during the time that shaft 94 has rotated tothe position whereby shutter 36 blocks its respective external feedbackbeam and cam 92 actuates switch 97 to produce a gating signal on line1M. Normally non-conducting gate 73 is rendered conductive by the gatingsignal. Phase detector 33 provides an output signal which is applied viaconducting gate 73 and integrator 39 to piezoelectric crystal 49,thereby positioning mirror 13 to bring the signal on line 27 into thedesired phase quadrature relationship with the signal on line 30.

Upon the completion of the alignment mode, shutter 36 is rotated out ofthe path of the respective external feedback signal, and cam 93 actuatesswitch 98 to produce a gating signal on line 102. The gating signalrenders conductive the normally non-conducting gates 72 and 74. If thearbitrary phase and amplitude of the external feedback signal from beamA to beam B are not correct, signals of appropriate polarity areproduced at the outputs of phase detectors 33 and 34 so as to positionmirror 10 long the direction of the ex temal feedback signal and in adirection perpendicular thereto, respectively, to reduce the outputsignals from phase detectors 33 and 34 to nulls in the same manner asdescribed in the case of mirror 9.

The manner in which the gating signals are generated in proper sequencecan be better understood by reference to FIG. 4. FIG. 4 shows on anenlarged scale the cam, switch and shutter components of FIG. 2.Corresponding elements are similarly numbered. Assuming, the sake ofexemplification that shaft 94 is rotating in the indicated clockwisedirection and momentarily is at the angular displacement shown, shutter36 blocks its respective external feedback beam while cam 92 actuatesswitch 97. This corresponds to the time of the alignment mode related tothe adjustment of mirror 10. Upon the incremental angular displacementof shaft 94 sufficient to disengage cam 92 and switch 97, switch 98becomes actuated by cam 93 and shutter 36 rotates out of the path of itsrespective external feedback beam allowing said beam to becomeestablished. Mirror 10 is positioned during the interval that cam 93continues to actuate switch 93. At the completion of said interval, cam93 disengages switch 98 and switch 95 becomes actuated by cam 90,initiating the alignment mode related to the positioning of mirror 9.Said alignment mode persists until cam disengages switch and switch 96becomes actuated by cam 91. The actual positioning of mirror 9 iscompleted during the time that cam 91 continues to engage switch 96. Anew cycle of operation commences when switch 96 is disengaged by cam 931and cam 97 again becomes actuated by cam 92.

It should be noted that shaft 94 preferably is one continuous shaft asshown in FIG. 4. The slight parallel displacement of the two portions ofshaft 94 shown in FIG. 2 are the result of the parallel displacement ofthe counterrotating beams A and B to facilitate distinguishing one beamfrom the other in the drawing. It is to be understood that there is noactual displacement between the axes of propagation of beams A and Beither inside or outside the ring laser nor is there necessarily anydisplacement between different portions of shaft 94.

A substantial reduction in the amount of apparatus required forminimization of the mode locking force acting between beams A and B isachieved in a second species of the invention by the technique of makingthe signals on lines 29 and 30 of FIG. 2 of equal amplitude and oppositephase rather than by eliminating said signals. Said technique causes thecoupling acting between beams A and B to become purely Hermitian asdiscussed in connection with he vector diagrams of FIGS. la and lb. Aspreviously pointed out, the total elimination of the skew Hermitiancomponent of the coupling force acting between beam A and beam B doesnot totally eliminate mode locking but it does effect a very substantialreduction therein. In accordance with the theory of the presentinvention, a single external feedback mirror (either mirror 9 or mirror10) is positioned along the direction of the respective externalfeedback path and in a direction perpendicular thereto so as tointroduce a skew Hermitian component in the cross coupling between beamsA and B equal in amplitude but opposite in phase to the skew Hermitiancomponent already present due to the internal feedback between thebeams. The desired result it achieved through the use of the relativelysimple structure represented in FIG. 5 comprising amplitude detectors 80and 81, 90 phase delay circuit 82, phase detector 83 and summing circuit84. In terms of FIG. 2, the apparatus of FIG. 5 replaces phase detectors31, 32, 33 and 34, gates 41, 43, 37, 72, 73, 43, and 74, shaft 94 andall of its associated elements, integrator 39, piezoelectric crystal4t), integrator 75, mirror 10, piezoelectric crystal 76, motor 77 andobviates the need for the reference signals on lines 27 and 28. Line 29of FIG. 2 is connected to one input of phase detector 83 and toamplitude detector 81 of FIG. 4 whereas line 30 of FIG. 2 is connectedto 90phase delay circuit 82 and amplitude detector 80 of FIG. 4. Theoutput of circuit 82 is connected to the second input of phase detector83. The outputs of amplitude detectors 80 and 81 are connected tosumming circuit 84. The output of circuit 84 of FIG. 4 is connected tomotor 44 of FIG. 2 and the output of phase detector 83 of FIG. 4 isconnected to integrator 42 of FIG. 2.

In operation, the signal on line 29 (representing the amplitudemodulation on beam A due to internal feedback from beam B) is rectifiedinto a signal of one polarity by amplitude detector 81 while the signalon line 30 (representing the amplitude modulation of beam B due tointernal feedback from beam A) is rectified into a signal of theopposite polarity by amplitude detector 80. The detected signals areapplied to summing circuit 84 which provides an output signal on line 85representing the amplitude difference between the signals on lines 29and 30. Said amplitude difference is related to the extent to which thecoupling between beams A and B is not purely Hermitian assuming that thesignals on lines 29 and 30 are of opposite phase. The amplitude errorsignal on line 85 is applied to motor 44 to vary the amplitude of theexternal feedback signal in the proper direction and amount to cause theoutput of circuit 84 to fall to a null. The phase of the externalfeedback signal is controlled by the output signal on line 86 which isapplied to integrator 42 to vary the position of mirror 9 along thedirection of the respective external feedback signal. The signals onlines 85 and 86 are driven to nulls only when the signals on lines 29and 30 are of equal amplitude and opposite phase which is the uniquecondition for the total elimination of any skew l-lermitian componentwhich may be present due to the internal feedback between beams A and Bwithin the ring laser.

The very considerable improvement effected by the relatively simpleapparatus of FIG. 4 is reflected in the data plotted in FIG. 6. Saiddata was obtained with a conventional ring laser operating with andwithout the external feedback afforded by a single external mirror, suchas minor 9 of FIG. 2. The abscissa of the plot of FIG. 6 is related tothe rotational rate of the ring laser about an axis perpendicular to theplane of the ring. The ordinate of the plot is related to the frequencyof the beat note produced by heterodyning the counterrotating beams ofthe ring laser in a conventional manner. The data of shaded curve 87 ofFIG. 6 was taken in the absence of any external feedback and clearlyshows that the frequency of the beat note varies for a given rotationrate of the ring laser and that the amount of frequency variationincreases as the ring rotational rate decreases, i.e., the range ofordinate values for a given abscissa value increases as the abscissavalue decreases. The frequency variations of the beat note in theabsence of external feedback are attributable to the random phasevariations of the internal feedback acting between two counterrotatingbeams within the ring laser.

Merely by the provision of an external mirror, such as mirror 9 in FIG.2, which is properly positioned so as to vary the amplitude and phase ofthe external feedback to make the signals on lines 29 and 30 of FIG. 2equal in amplitude but opposite in phase, the performance depicted incurve 88 is achieved. It should be noted in the presence of externalfeedback of proper amplitude and phase, the objectionable frequencyvariation of the beat note at a given angular rotational rate of thelaser is substantially eliminated. Moreover, the relationship betweenbeat note frequency and ring rotational rate is substantially linearizedrelative to the relationship obtaining in the absence of externalfeedback as depicted by curve 87. Additionally, external feedback ofproper amplitude and phase permits the generation of a useful beat notesignal whose frequency is accurately representative of ring rotationalrates to much lower values of rotational rates than is possible in theabsence of external feedback.

While the invention has been described in its preferred embodiments, itis to be understood that the words which have been used are words ofdescription rather than limitation and that changes within the purviewof the appended claims may be made without departing from the true scopeand spirit of the invention in its broader aspects.

We claim:

1. A ring laser producing two counterrotating laser beams,

said laser beams being extracted and made available along respectivepaths outside the ring cavity of said laser,

said extracted beams being amplitude modulated due to cross-couplingbetween said laser beams inside said cavity,

first means located outside said cavity along one of said paths forredirecting energy from one of said extracted beams back into saidcavity in the direction of the other of said beams so that energy fromsaid one beam is coupled to said other beam inside said cavity,

null-seeking control means for controlling said first means to vary theredirected energy, and

second means located along another of said paths for detecting theamplitude modulation on the other of said extracted beams and producingan output signal in response thereto,

said output signal being applied to said control means to vary saidredirected energy.

2. A ring laser as defined in claim 1 wherein said nullseeking controlmeans varies the amplitude of the redirected energy.

3. A ring laser as defined in claim 1 wherein said nullseeking controlmeans varies the phase of the redirected energy.

4. A ring laser as defined in claim 1 wherein said nullseeking controlmeans varies the amplitude and the phase of the redirected energy.

5. A ring laser as defined in claim 1 wherein said output signal isapplied to said control means to vary said redirected energy so thatsaid amplitude modulation is reduced to a minimum.

6. A ring laser as defined in claim 1 and further including third meanslocated along another of said paths for detecting the amplitudemodulation on said one of said extracted beams and producing an outputsignal in response thereto,

both said output signals from said second and third means being appliedto said control means to vary said redirected energy so that theamplitude modulation on one of said beams is made equal in amplitude andopposite in phase to the amplitude modulation of the other of said laserbeams.

l I! i

1. A ring laser producing two counterrotating laser beams, said laserbeams being extracted and made available along respective paths outsidethe ring cavity of said laser, said extracted beams being amplitudemodulated due to crosscoupling between said laser beams inside saidcavity, first means located outside said cavity along one of said pathsfor redirecting energy from one of said extracted beams back into saidcavity in the direction of the other of said beams so that energy fromsaid one beam is coupled to said other beam inside said cavity,null-seeking control means for controlling said first means to vary theredirected energy, and second means located along another of said pathsfor detecting the amplitude modulation on the other of said extractedbeams and producing an output signal in response thereto, said outputsignal being applied to said control means to vary said redirectedenergy.
 2. A ring laser as defined in claim 1 wherein said null-seekingcontrol means varies the amplitude of the redirected energy.
 3. A ringlaser as defined in claim 1 wherein said null-seeking control meansvaries the phase of the redirected energy.
 4. A ring laser as defined inclaim 1 wherein said null-seeking control means varies the amplitude andthe phase of the redirected energy.
 5. A ring laser as defined in claim1 wherein said output signal is applied to said control means to varysaid redirected energy so that said amplitude modulation is reduced to aminimum.
 6. A ring laser as defined in claim 1 and further includingthird means located along another of said paths for detecting theamplitude modulation on said one of said extracted beams and producingan output signal in response thereto, both said outpuT signals from saidsecond and third means being applied to said control means to vary saidredirected energy so that the amplitude modulation on one of said beamsis made equal in amplitude and opposite in phase to the amplitudemodulation of the other of said laser beams.